J. Phys. Chem. 1981, 85, 2607-2611
to relate the concentrations to each other absolutely. Accumulated uncertainties are therefore in excess of 10% even for examples where the molecular dipole moment (i-e., transition moment) is known with reasonable accuracy from microwave spectroscopy. Fortunately the determination of radical concentrations from LMR follows similar procedures developed over a decade ago for kinetic applications of gas-phase EPR and, although laborious, the determination of line shapes and areas is well understood. Reactions of the important atmospheric species HOP have been particularly well studied by far-infrared LMR. The technique is advantageous for HOPkinetics due to its high sensitivity, lo9cm-3for the ground state, and capacity to detect related species such as OH simultaneously. For example, the reaction HOP + NO = OH NO2 has now been studied by LMR in three laboratories33$35936 with good agreement for the rate constant and with measurements by other techniques. The temperature dependence of this reaction has also been measured36 by incorporating a heated flow reactor before the LMR detection region, again in an analagous fashion to earlier experiments using EPR. The majority of the kinetic results obtained so far have used the discharge laser sources but as the optically pumped lasers are developed for kinetics a much wider variety of radical reactions should be amenable to study. Pioneering results on the chemistry of the methoxy radical are an indication of future kinetic research with these
+
(35)C. J. Howard, J. Chem. Phys., 71, 2352 (1979). (36)J. P. Burrows, D. I. Cliff, G. W. Harris, B. A. Thrush, and J. P. T. Wilkinson, h o c . R. SOC.London, Ser. A, 368, 463 (1979).
2607
lasers.37 Finally, it is interesting to note that all the kinetic applications so far have used far-infrared lasers and there appears to be no fundamental reason why mid-infrared spectrometers cannot be converted for kinetic studies also. Conclusion The rapid and successful development of LMR is now manifested by the many instruments in use in more than a dozen laboratories throughout the world. The continuing discoveries of new laser lines in the far-infrared provides an almost continuous frequency coverage in the region and it is reasonable to postulate that "tuning" transitions from one laser line to the next across the 100-1000-~mregion should be possible in the near future. This is fortunate as in the far-infrared there are no narrow-band tunable laser sources for spectroscopy at zero field, and LMR is presently the only technique available for spectroscopy of free radicals in this region. Although discoveries of new laser lines in the mid-infrared have not been forthcoming there are alternative tunable sources, particularly the semiconductor diode laser, to cover this region for highresolution free-radical spectroscopy.
Acknowledgment. I express my gratitude to many colleagues in North America and Europe for extensive correspondence and discussions on LMR over the past five years. This work has been generously supported at Cambridge by the Science Research Council and the Royal Society, and in Gottingen by the Max Planck Gesellschaft. (37)H. E.Radford, Chem. Phys. Lett., 71,195 (1980).
ARTICLES Flexible d Bask Sets for Sc through Cu Anthony
K. Rappe, Terry A. Smedley,+ and Wllliam A. Goddard, 111"
Arthur Amos Noyes Laboratory of Chemical Physlcs, t Calltornla Instltute of Technolcgy, Pasadena, Calliornla 9 1125 (Received: September IO, 1980: In Flnal Form: May 27, 1981)
A prescription is presented and implemented for Sc through Cu that leads to practical-sized Gaussian d basis seb capable of accurate descriptions of the srndn-'"states of the atom. Optimized Gaussian basis seta containing . four, five, and six primitives are given along with recommended double zeta, double zeta, and triple zeta contraction schemes, respectively. It is suggested that these basis sets be used for calculationson large, medium, and small transition metal complexes, respectively.
Introduction In molecular calculations involving transition metals, it is important to retain the smallest number of d basis functions consistent with accurate descriptions of the d orbitals of the atoms and molecules. The reasons are that integral calculations for d functions are costly and also that tITT Rayonier, Inc., Grays Harbor Division, Hoquiam, WA 98550. * Contribution No. 6304.
each additional set of d primitives normally leads to six additional Cartesian Gaussians for SCF calculations. Based on atomic calculations, it has been concluded that five sets of d primitive Gaussians [denoted as (5d)l are required to accurately describe the shape of the atomic d orbitals. [For some applications a properly determined (4d) basis wiU be adequate.] For example, the total energy of the d10 state of Ni drops by 5.99,5.74,1.57, and 0.14 eV upon going from three d's to four d's to five d's to six d's to seven ds, respectively. Of special concern in variational 0 1981 American Chemical Society
2608
The Journal of Physical Chemistry, Vol. 85,No. 18, 1981
Rappe et al.
TABLE I: Atomic Excitation Energies (eV) Relative t o the s2dn-2Statea
atom
state
sc
s1d2 d3 s1d3 d4 s'd9 d5 s1d5
Ti
V Cr
d6 Mn Fe co
s1d6 d7 s1d7 ds s'd' d9
Ni
s1d9
cu
sld10
d" d" a
s2d?l-2
(4dY opt. for sod"
(5d)* augmented
(5dIC opt. for sodn
(6d)d augmented
(6dIC opt. for sodn
1.54 6.87 1.17 6.82 0.85 5.94 -0.50 9.10 4.37 13.04 2.84 11.43 2.63 11.21 2.44 9.80 0.85 8.40
1.25 4.97 0.73 4.76 0.29 3.86 -1.11 6.44 3.43 9.98 1.96 8.49 1.71 8.24 1.53 6.99 -0.08 5.49
1.08 4.58 0.60 4.34 0.16 3.33 -1.21 5.82 3.32 9.15 1.79 7.44 1.51 7.01 1.25 5.41 -0.42 3.72
1.08 4.61 0.61 4.45 0.17 3.44 - 1.22 5.97 3.36 9.37 1.83 7.77 1.57 7.39 1.32 5.84 -0.31 4.31
1.03 4.52 0.54 4.28 0.15 3.31 - 1.24 5.79 3.34 9.18 1.80 7.47 1.53 7.06 1.27 5.47 -0.38 3.79
1.02 4.51 0.55 4.29 0.13 3.32 - 1.25 5.81 3.33 9.21 1.81 7.51 1.52 1.07 1.29 5.56 -0.36 3.91
(5dIb opt. for
Uncontracted basis sets were used in all cases.
Wachter, ref 2.
This work.
numerical HF
1.01 4.47 0.54 4.25 0.12 3.27 - 1.27 5.75 3.33 9.15 1.80 7.46 1.53 7.05 1.28 5.47 -0.37
Hay, ref 5.
TABLE 11: Exponents and Contraction Coefficients for the ( 4 d ) d Basis Sets C
01
C
01
oi
V
Ti
sc
8.614 2.056 0.5107
6.40051 7 23D-02 2.627 056471)-01 4.75394469D-01
9.810 2.433 0.6451
7.66199122D-02 2.94478935D-01 4.89296 130D-0 1
12.02 3.034 0.8298
0.1024
5.92246514D-01
0.1407
5.26968 156D-01
0.1895
Cr
14.07 3.587 0.9899 0.2237
7.87628253D-02 3.08352315D-01 4.99861905D-01 4.89872992D-01
0.2662
20.67 5.399 1.527 0.3477
8.3.8823383D-02 3.20288911D-01 5.05192903D-01 4.65718825D-01
7.98180297D-02 3.11699068D-01 5.01003803D-01 4.81616287D-01
18.40 4.772 1.342 0.3071
Ni
co
23.15 6.071 1.725 0.3984
4.59207328D-01
Met hod In Table I we compare the separations of the s2dn-2, sldn-l, sod" states of Sc-Cu for Hartree-Fock (HF) calculations with various d basis sets. For Ni (3F, 3D, and 'S (1) Dunning,Jr., T. H.;Hay, P. J. In "ModernTheoretical Chemistry"; Schaefer, 111, H. F., Ed.; Plenum Press: New York, 1977; Vol. 3, p 1. (2) Wachters, A. J. H. J. Chem. Phys. 1970,52, 1033. (3)Roos, B.;Veillard, A.; Vinot, G. Theor. Chim. Acta 1971,20, 1.
8.09 36 79 8 1D-0 2 3.17 08663 1D-01 5.0267 1338D-01 4.72354408D-01 cu
8.22209743D-02 3.23241646D-01 5.05380400D-01
calculations is that the primitive basis allows a compact contraction to reduce the number of independent functions. Previous studies' have shown that a five-Gaussian basis can be contracted to two functions, [5/2], often referred to as double zeta, without affecting calculations on molecules, whereas a six-Gaussian basis set cannot be acceptably contracted to two functions [6/2]. For these reasons, the (5d) basis has been considered an ideal one for molecular calculations of first-row transition metals. Unfortunately the standard (5d) basis sets2%are not sufficiently flexible to describe all the important states of transition metals. For example, they lead to an error of 4 eV in the s2d8-d10splitting of Ni. In this paper we report (4d), (.!id), and (6d) basis sets for the first transition row (Sc-Cu) and double zeta, double zeta, and triple zeta contractions of the (4d), (5d), and (6d) basis sets, respectively, for these atoms.
4.99 74 4 1 61D-0 1 Fe
Mn
16.18 4.183 1.169
7.7 4 048 182D-02 3.02137513D-01 4.96 182 2 16D-0 1
26.22 6.857 1.955 0.4472
8.07 28 59 11D-02 3.23000241D-01 5 .08 297 497D-0 1 4.5 7 65 87 0 6D -0 1
states) exact (numerical) HF calculations lead to an s2d8-dlosplitting of 5.47 eV, whereas the Wachter basis (5d optimized for s2d8)leads to 9.80 eV, an error of 4.3 eV! On the other hand, by optimizing the d basis for the sodlo state, we obtain s2d8-d10splittings of 6.99 (4d), 5.84 (5d), and 5.56 eV (6d), with errors of 1.52, 0.37, and 0.09 eV, respectively. The origin of this effect is as follows. The d orbitals are small in size compared with the s orbitals, so than an electron in the 4s orbital does not effectively shield a 3d electron from the nucleus. Thus in the d10 state each d electron is much more effectively shielded from the nucleus than in the s2d8state, leading to larger (more diffuse) orbitals. Consequently, the 5d basis from s2d8is not sufficiently diffuse to describe the d orbitals of the d10 state. On the other hand, the 5d basis from the dO ' state can describe the tighter orbitals of the s2d8state by merely changing the linear coefficients. Further, the dlO-optimized basis provides a better description of the 3d-4s interactions, which is evidenced by improvement in the Koopmans' theorem ionization potentials for the 4s orbital of both the s2d8and slds states. The 4s orbital energies (hartrees) for the s2d8state are 0.276 25 for numerical HF, 0.278 483 for dlO-optirnized (5d) basis, and 0.270 857 for Wachter's (5d) basis. For the sldOstate, the 4s orbital energies are 0.23576 for numerical HF, 0.236990 for d'O-optimized basis, and 0.217 732 for Wachter's basis. The
The Journal of Physical Chemistry, Vol. 85, No. 18, 198 1
Flexible d Basis Sets for Sc through Cu
2609
TABLE 111: Exponents and Contraction Coefficients for the (Sd) d Basis Sets
C
a
C
a
C
2.89190492D-02 1.49174065D-01 3.34660015D-01 4.60697426D-01
20.73 5.090 1.545 0.4585
2.66517493D-02 1.46864218D-01 3.40392761D-01 4.56804981D-01
21.18 5.566 1.753 0.5256
V 3.35595342D-02 1.64 56749OD-0 1 3.6579 1138D-01 4.58772599D-01
4.656 10383 D-0 1 Cr
0.1102
4.46199540D-01
0.1336
3.87748639D-01 Fe
2.82278486D-02 1.53903211D-01 3.68 45 113 OD-0 1 4.68309376D-01
28.15 7.564 2.410 0.7282
3.42869181D-02 1.70996105D-01 3.79828354D-01 4.58334035D-01
31.78 8.426 2.719 0.8335
3.54066628D-02 1.78115212D-01 3.8343646D-01 4.5 1535378D-01
3.68 37 6780D-0 1
0.2113
a
Ti
sc
15.19 3.710 1.084 0.2974 0.06936 28.00 7.213 2.241 0.6612 0.1620
3.91055232D-01
Mn
0.1799
co 34.97 9.463 3.051 0.9365
3.622 9 38 12D-02 1.81096242 D-0 1 3.90 134959D-0 1 4.509 39364 D-0 1
0.2350
3.49816738D-01
39.49 10.75 3.475 1.065 0.2641
3.59074071D-01
cu
Ni
3.55460797D-02 1.79996302D-01 3.92 560290D-01 4.54418307D-01 3.44670087D-01
43.66 11.97 3.916 1.222 0.3066
3.56934638D-02 1.80263235D-01 3.896 IO 112D-0 1 4.50798523D-01 3.464025231)-01
TABLE IV: Exponents and Contraction Coefficients for the ( 6 d ) d Basis Sets
C
a
C
a
a
C
23.24 6.143 2.007 0.6652
1.43632903D-02 7.80683128D-02 2.17559770D-01 3.49798322D-01
28.11 7.630 2.528 0.8543
1.53148419D-02 8.40269549D-02 2.38297448D-01 3.77444967D-01
33.36 9.331 3.158 1.113
0.2021
4.25010943D-01
0.2673
4.12163691D-01
0.3608
V 1.53978328D-02 8.463961811)-02 2.40000837D-01 3.793783331)-01 4.08820800D-01
0.05454
3.72481407D-01
0.0743
3.17466802D-01
0.1007
3.01703363D-01
Ti
sc
Mn
Cr
37.89 10.58 3.603 1.270 0.4118 0.1126
42.63 11.97 4.09 1 1.450
4.00116732D-01
0.4700
3.944439 55D-01
0.5100
2.8 7 349938D-01
0.1281
2.73536085D-01
0.1382
co 51.69 14.70 4.851 1.643
Fe
1.61917253D-02 9.007 14944D-02 2.52220408D-01 3.87985843D-01
1.78005661D-02 1.04596888D-01 2.97 33016 1D-0 1 4.23527577D-01
1.67152191D-02 9.40154390D-02 2.60779605D-01 3.9367 87 6 1D-0 1
47.10 13.12 4.478 1.581
3.86216164D-01 2.54090511D-01
cu
Ni
58.73 16.71 5.783 2.064
1.7 640879 1D-02 1.00782742D-01 2.74366978D-01 4.01473873D-01
1.752926 15D-02 1.00405051D-01 2.76091985D-01 4.03476707D-01
65.80 18.82 6.538 2.348
1.707 88632D-02 9.91554497D-02 2.74753795D-01 4.04008442D-01
0.5075
3.72830506D-01
0.6752
3.81219977D-01
0.7691
3.82620040D-01
0.1433
2.18673606D-01
0.1825
2.502557 29D-01
0.2065
2.49008434D-01
improvement in the s1d9ionization is due to a better description of the tail region of the 3d orbital. From such considerations we conclude that d basis for transition metals should be optimized for the d” configuration rather than for the ground-state configuration and that a (4d) basis optimized in this manner should yield adequate results for molecular calculations. Using the (149, 9p) primitive sets of Wachter (uncontracted), we optimized (5d) and (6d) basis sets for the d” states of Sc, Ti, V, Cr, Mn, Fe, Co, Ni, and Cu leading to the results in Tables II-IV. (For Cu the d basis was optimized for the dll state. Although this state is not allowed by the Pauli principle, it leads to a basis consistent with the trends across the row.)
new (5d) basis gives energy splittings in reasonable agreement with numerical HF (considerably better than with the Wachter basis), and the new (6d) basis gives energy splittings in good agreement with numerical HF. For example, the Wachter’s (5d) basis for Ni yields an sldg s2d8splitting of -2.44 eV, our reoptimized (5d) basis gives -1.32 eV, and our reoptimized (6d) basis yields -1.29 eV, compared with -1.28 eV for numerical HF. Further, if uncontracted primitives are used, the reoptimized basis sets apparently perform about as well as augmented basis sets.6i6 For example, the augmented basis of Hay yields s1d9 s2ds splittings of -1.25 (5d) and -1.27 (6d). There are two significant differences between the augmentation approach and the current technique. The
Discussion In all cases the reoptimized (5d) basis is considerably more diffuse than Wachter’s, and the resulting energy separations are much improved. As shown in Table I, the
(4) Roos, B.; Veillard, A.; Clementi, E. “A General Program for Calculation of Atomic SCF Orbitals by the Expansion Method”,SpecialIBM Technical Report, IBM Research Laboratory: San Jose, CA, 1968. (5) Hay, P.J. J . Chem. Phys. 1977, 66,4377. (6) Brooks, B. R.; Schaefer, 111, H. F. Mol. Phys. 1977,34, 193.
-
-
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The Journal of Physical Chemistty, Vol. 85, No. 18, 1981
Rappe et al.
Hartree-Fock Atomic Energies for Various d Orbital Basis Sets (in hartrees) Szdn-a sodn sodn atom state opt. (5d)b augmented ( 5 d p opt. (5d)C augmented (6d)a opt. (4d)C
TABLE V:
SC Ti V Cr Mn Fe CO
Ni CU
a
sad1 s'd2 d3 sZd2 s1d3 d4 sad3 S1d4 d5 sad4 ~'d' d6 sad5 S1d6 d' sad6 s1d7 d8
-759.722 877 -759.666 277 -759.470 540 -848.389 292 -848.346 499 -848.138 608 -942.862 874 -942.831 640 -942.644 716 - 1043.282 630 - 1043.301 167 -1042.948 1 7 1 -1149.832 454 -1149.671 881 -1149.353 107 - 1262.401 375 -1262.296 914 - 1261.981 298 -1381.361 715 -1381.265 186 -1380.949 590 -1506.807 232 -1506.717 474 -1506.447 106 -1638.875 124 -1638.843 721 -1638.566 483
sad7
s1d8 d9 sada s d d" sad9 S'd'O d"
Hay (ref 5).
-759.719 586 -759.679 887 -759.551 165 -848.379 808 -848.357 829 -848.220 246 -942.845 727 -942.839757 -942.723 174 - 1043.256 202 - 1043.300 676 -1043.042 401 -1149.794 112 -1149.672 122 -1149.457 736 - 1262.348 502 -1262.282 798 - 1262.074 920 -1381.291 278 -1381.235765 -1381.033 643 -1506.716 234 -1506.670 449 -1506.517 245 -1638.760 929 -1638.776 189 - 1638.624 108
Wachters (ref 2).
-759.708 393 -759.720 942 -759.662 328 -759.681 142 -759.525 599 -759.551 582 -848.385 713 -848.358 202 -848.363 335 -848.331 298 - 848.183 448 -848.222 278 -942.815 540 -942.857 312 -942.851 168 -942.804 944 -942.673 704 -942.731 023 - 1043.210 758 - 1043.272 889 -1043.251 598 -1043.317 776 -1042.974 216 -1043.053 370 -1149.734 035 -1149.818 974 -1149.607 819 -1149.695 588 -1149.367 450 -1149.474 515 -1262.276 115 -1262.386 692 -1262.204 266 -1262.319 432 - 1261.963 960 -1262.101 054 - 1381.202 241 -1381.343 322 - 1381.139 353 -1381.285 779 - 1380.899 584 -1381.071 922 -1506.616 160 - 1506.784 930 -1506.559 786 - 1506.736 591 - 1506.359 442 - 1506.570 219 - 1638.642 279 - 1638.852 7 0 8 - 1638.645 090 -1638.864 136 - 1638.440 407 - 1638.694 281
-759.725 081 -759.687 210 -759.558 873 -848.392 713 -848.372 1 0 1 -848.234 826 -942.867 788 -942.862 453 -942.746 332 - 1043.289 092 -1043.334 813 -1043.076 263 -1149.840 173 -1149.717 585 -1149.502 915 -1262.411 565 -1262.345 366 -1262.136874 -1381.374 104 -1381.317 856 -1381.114 835 -1506.822 086 - 1506.775 254 - 1506.620 980 - 1638.893 156 - 1638.907 196 - 1638.753 923
sodn opt. (6d)C -759.724 870 -759.687 207 -759.559 214 -848.392 637 -848.372 335 -848.234 978 -942.868 703 -942.863 776 -942.746 878 - 1043.290 634 - 1043.336 700 -1043.077 209 -1149.842 561 -1149.720 018 -1149.504 136 -1262.415 316 -1262.348 980 -1262.139 278 -1381.376 147 -1381.320 418 -1381.116 288 -1506.832 221 -1506.784 842 -1506.627 784 - 1638.907 041 - 1638.920 097 -1638.763 533
This work.
TABLE VI: Total Energies (hartrees) and Errors (eV) for Various Contraction Schemes of Nickel s2d8 basis current (4d) .
I
Hay (5d)
TE
A
(3.1) . . . s'd' s1d9 dl' ( 4 , l ) sad8 s1d9
-1506.616 160 -1506.616 083 - 1506.616 155 - 1506.716 234 -1506.698 446 -1506.673 713 -1506.784 930 - 1506.782 602 - 1506.781 031 - 1506.822 086 -1506.798 101 - 1506.762 230 -1506.832 221 - 1506.821 850 - 1506.809 744 -1506.822 086 - 1506.822 026 -1506.821 940 - 1506.832 221 -1506.832 216 - 1506.832 219
0.0 0.002 0.000 0.0 0.490 1.157 0.0 0.063 0.106 0.0 0.653 1.629 0.0 0.282 0.612 0.0 0.002 0.004 0.0 0.000 0.000
d lo
current (5d)
( 4 , l ) >d' s1d9 dIa
current (6d)
( 5 , l ) sads s1d9
Hay (6d)
(4,1,1) sada s1d9 d" (4,1,1) sada s1d9 d'O
dl'
current (6d)
s1d9
contraction
current (5d) basis is easily contractable to double zeta (vide infra), and the total energies (as shown in Table V) for all three states for each atom are as low (if not significantly lower) for the current basis as for the comparable augmented basis. The second point implies that the current basis sets are more "consistent" than those generated through augmentation. For example, for Ni the current (5d) basis has a total energy 1.87 eV lower than the (5d) augmented basis, and the current (6d) basis has a total energy 0.28 eV lower than the (6d) augmented basis. Another symptom of consistency is that in all cases our excitation energies are higher than numerical HF (the expected ordering for an incomplete basis) and the accuracy of the excitation energies increases as the size of the basis increases (as expected for an incomplete basis), whereas the augmented basis sets yield excitation energies
TE -1506.559 -1506.559 -1506.559 -1506.653 -1506.670 -1506.665 -1506.734 -1506.736 -1506.736 -1506.752 -1506.775 -1506.767 -1506.774 -1506.784 -1506.782 -1506.775 -1506.775 -1506.775 -1506.784 -1506.784 -1506.784
708 786 719 027 449 198 236 591 376 188 254 389 662 842 546 192 254 235 837 842 835
d" A
TE
A
0,002 0.0 0.000 0.474 0.0 0.143 0.064 0.0 0.006 0.628 0.0 0.214 0.277 0.0 0.062 0.002 0.0 0.001 0.000 0.0 0.000
- 1506.359 439 - 1506.359 375 - 1506.359 443
0.000 0.002 0.0 1.096 0.138 0.0 0.108 0.006 0.0 1.479 0.201 0.0 0.588 0.061 0.0 0.001 0.001
-1506.476 954 -1506.512 184 -1506.517 245 - 1506.566 259 - 1506.570 002 - 1506.570 219 - 1506.566 627 -1506.613 610 -1506.620980 -1506.606 164 -1506.625 536 - 1506.627 784 - 1506.620 8 3 1 - 1506.620 961 - 1506.620 980 -1506.627 781 -1506.627 777 -1506.627 784
0.0 0.000 0.000 0.0
both low and high relative to numerical HF, indicating that in some cases the augmentation procedure leads to a differential bias against the s2dn-2state. Because of the costs involved, nearly all molecular calculations with transition metals are carried out with contracted basis sets. We propose herein a (3,l) contraction of the reoptimized (4d) basis set, a (4,l) contraction of the reoptimized (5d) basis set, and a (4,1,1) contraction of the reoptimized (6d) basis. The contraction coefficientslisted in Table I1 are based upon the 3dn states of the atoms. As shown in Table VI for Ni, various contraction schemes yield remarkably different results. As is apparent, the only double zeta contraction schemes that are truly acceptable are the (3,l) and (4,l) contractions of the reoptimized (4d) and (5d) basis sets. Both of the triple zeta contraction schemes are acceptable, though the cur-
J. Phys. Chem. 1981, 85, 2611-2613
rent (6d) basis yields the best total energy and hence is the basis of choice. A fundamental problem with double zeta contractions of the augmented basis sets is that they fix the ratio of coefficients between all original primitives and allow only the relative coefficients of the (slightly used) diffuse augmenting primitives to vary. While the contraction of this augmented basis by means of orbitals from the 4s13d"-l state leads to perhaps acceptable atomic splittings [errors of 0.49 eV (5d) and 0.65 eV (Sd)], it is not flexible enough to handle the general contraction or expansion of the 3d orbitals that result from a charge transfer to and from the ligands in molecules. For this reason we find the reoptimized (5d) basis contracted (4,l) to be the most suitable for routine molecular calculations. Further, we suggest that the (4d) basis for calculations on large transition metal complexes is a useful basis (errors
2611
in excitation energies of less than 1.5 eV and no difficulty contracting to double zeta). Acknowledgment. This research was supported in part by the U.S.Department of Energy (Contract No. EX-76G-03-1305). However, any opinions, findings, conclusions, or recommendations expressed herein are those of the authors and do not necessarily reflect the views of DOE. Partial support was also provided by the National Science Foundation (Grant No. CH&80-17774). The research reported in this paper made use of the Dreyfus-NSF Theoretical Chemistry Computer which was funded through grants from the Camille and Henry Dreyfus Foundation, the National Science Foundation (Grant No. CHE78-20235), and the Sloan Fund of the California Institute of Technology.
Conformational Equilibria in trans-I ,2-Diarylethylenes Manifested in Their Emission Spectra. 4.' 3-Anthryl and 3-Pyrenyl Derivatives Gabrlella Flscher and Ernst Flscher" Depadment of Structural Chemistry, Weizmann Institute of Science, Rehovot, Israel (Received: December 18, 1980; In Final Form: May 12, 1981)
The emission spectra of the title compounds vary with the wavelength of excitation. They can be described as superpositions of two spectra shifted 8-15 nm with respect to each other and contributing to the overall emission to an extent varying with the excitation wavelength. The phenomenon is ascribed to the existence, in solution, of an equilibrium mixture of two almost isoenergetic rotational conformers with slightly different absorption and emission spectra.
In earlier papers by us1 and by Sheck et aL2emissionspectroscopic evidence was described for the existence of conformational equilibria in solutions of 2-naphthyl and 3-phenanthryl analogues of stilbene. In order to check
TABLE I: Emission Peaks (in n m ) of the Two Modifications J. and t of Various trans-(3-Anthry1)ethylenes under the Conditions Described in Figure la compd
la
lb
the generality of the underlying concepts, we have now investigated a number of 3-anthryl derivatives. As expected by analogy, we observed in all of them a variation of the emission spectra with the wavelength of the exciting light, which was most pronounced at long excitation wavelengths, in the tail of the absorption bands. In all (1) (a) Fischer, E. J. Phys. Chem. 1980, 84, 403-410. (b) Bull. SOC. Chirn. Belg. 1979, 88, 889-895. (c) Haas, E.; Fischer, G; Fischer, E. J. Phys. Chem. 1978,82,1638-43. (d) Fischer, G Fischer, E. Unpublished observations at 25 O C , not at reduced temperatures. (Improved experimental conditions have enabled ua to make these observations recently.) (2) Scheck, Yu. B.; Kovalenko, N. P.; Alfimov, M. V . J. Lumin. 1977, 15. 157. 0022-3654/81/2085-26 11$0 1.2510
1 t 1 t
IC
.1
Id
t J. t
2a
4
2b
t J. t
2c
1
t 2d
&
t
413 426 407 416 414 4 24 423 430 422 431 4 15 428 426 433 423 433
436 452 (432) 444 438 451 448 458 450 460 442 457 450 459 450 462
462 482 (461) 414 (468) 482 (479) (492) 480 490 470 488 (483) (493) 419 497
Values in parentheses are n o t well defined.
cases the emission spectra can be described by a superposition of two sets of peaks, shifted by 8-15 nm with respect to each other, and with the relative contributions of each set to the overall spectrum varying with the wavelength of excitation. Figure 1describes the results obtained at reduced temperatures, where the spectra are sharper, but qualitatively similar results were obtained also at room temperature. 0 1981 American Chemical Society
